浅埋隧道围岩应力场的计算复变函数求解法

›› 2010, Vol. 31 ›› Issue (S1): 86-90.

浅埋隧道围岩应力场的计算复变函数求解法

王志良¹，申林方²，姚激³，高成杰⁴

1.同济大学地下建筑与工程系，上海 200092；2.中国科学院武汉岩土力学研究所，武汉 430071； 3.昆明理工大学工程力学系，昆明 650024；4.北京市环境保护科学研究院，北京 100037

收稿日期:2010-04-23 出版日期:2010-08-10 发布日期:2010-09-09
作者简介:王志良，男，1982年生，博士研究生，主要从事岩土工程与地下结构的研究工作。
基金资助:
云南省应用基础研究计划项目（No. KKSA200806040）。

WANG Zhi-liang¹, SHEN Lin-fang², YAO Ji³, GAO Cheng-jie⁴

1. Department of Geotechnical Engineering, Tongji University, Shanghai 200092, China; 2. Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan 430071, China; 3. Department of Engineering Mechanics, Kunming University of Science and Technology, Kunming 650024, China; 4. Beijing Municipal Research Institute of Environmental Protection, Beijing 100037, China

Received:2010-04-23 Online:2010-08-10 Published:2010-09-09

摘要/Abstract

摘要：

对于受地表边界和地面荷载影响的浅埋隧道的围岩应力场，由于在数学处理上存在一定的困难，很难用解析解来进行分析，而通常采用边界元或有限元的数值方法来解答。为了求解浅埋隧道的应力场，采用边界配点来确定边界条件，同时用保角映射将一个含圆孔的半无限空间区域映射为圆环域，然后把这个区域内的解析函数展开成Laurent级数的形式，利用Muskhelishvili的复变函数理论和最小二乘法来确定解析函数的各项系数，从而求得浅埋隧道围岩压力的半数值、半解析解，最后通过算例给出了围岩应力的分布情况。计算结果表明，该方法计算精度高、计算量小，具有应用价值。

关键词: 保角映射, 复变函数, 浅埋隧道, 半数值半解析解, 计算复变函数法

Abstract:

Due to the influence of surface boundary and ground loads, the analysis of surrounding rocks of shallow tunnel is difficult by mathematic method. The analytic solution is too difficulty to obtain, so many solutions were obtained by using boundary element method or finite element method. In order to obtain stress field in surrounding rocks of shallow tunnel, the boundary condition is determined by setting finite points; the considered region in the physical plane is mapped to a circular ring region in the image plane by using the complex conformal transformation; and then the analytic functions are expanded into Laurent series; the Laurent series’ coefficients is obtained by using the function of complex variable method founded by Muskhelishvili and the least square method. The semi-analytical and semi-numerical solution of shallow tunnel’s stress field could be obtained by putting the Laurent Series’ coefficients into equation. Finally, the stress of surrounding rocks is depicted through an example. The results show that the computational function of complex variable method is precise, efficient and applicable.

Key words: conformal mapping, function of complex variable, shallow tunnel, the semi-analytical and semi-numerical solution, computational function of complex variable method

中图分类号:

U 451

王志良，申林方，姚激，高成杰. 浅埋隧道围岩应力场的计算复变函数求解法[J]. , 2010, 31(S1): 86-90.

WANG Zhi-liang, SHEN Lin-fang, YAO Ji, GAO Cheng-jie. [J]. , 2010, 31(S1): 86-90.

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